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Subsequent Event (Details) - CHINA - USD ($) $ in Thousands | 3 Months Ended | 12 Months Ended
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Apr. 02, 2022 | Jan. 01, 2022
Subsequent Event [Line Items] |  |
Carrying value of facility and land use right |  | $ 5,264
Land and Building |  |
Subsequent Event [Line Items] |  |
Expected proceeds from sale of facility and land use rights |  | $ 25,140
Down payment (percentage) |  | 25.00%
Period of recognition of gain on sale and a receivable for remaining amount of sales proceeds (in years) |  | 2 years
Land |  |
Subsequent Event [Line Items] |  |
Expected payments for land use right |  | $ 3,719
Subsequent event | Forecast | Land and Building |  |
Subsequent Event [Line Items] |  |
Down payment (percentage) | 6.00% |

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- Definition Expected Payments To Acquire Property, Plant, And Equipment + References No definition available. + Details
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Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Expected Proceeds From Sale Of Property, Plant, And Equipment + References No definition available. + Details
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Namespace Prefix: | kai_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Definition Proceeds From Sale Of Property, Plant, And Equipment, Maximum Period For Full Receipt, Period Post Effective Date + References No definition available. + Details
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- Definition Sale Of Property, Plant, And Equipment, Down Payment, Percent Received + References No definition available. + Details
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- Definition Carrying amount as of the balance sheet date of investments in land and buildings held for sale, excluding real estate considered to be inventory of the entity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03.1(f)) -URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910 + Details
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Namespace Prefix: | us-gaap_
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Balance Type: | debit
Period Type: | instant

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- Definition Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event. + References No definition available. + Details
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Period Type: | duration

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- Details
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Namespace Prefix: |
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- Details
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Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
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- Details
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- Details
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